In general, we employ physical and mathematical methods to understand the biophysics of cellular processes. For the past several years, emphasis has been on the biogenesis of coated vesicles involved in clathrin mediated endocytosis (CME) and other intracellular transport processes. CME is the principal pathway for the regulation of receptors, and internalization of certain nutrients and signaling molecules, at the plasma membrane of eukaryotic cells. Defects in CME can lead to metabolic disorders, aberrant signaling related to various cancers, and neurological disorders. A second major research area involves using published neurophysiological data to develop deeper basic understanding of the biophysical behavior of cell membranes at the normal (growth or gestation) temperatures of organisms (see below). Additionally, in the recent past we have collaborated on the development of a mathematical model to explore how difference in the average number of parasites (merozoites) released from malaria-infected blood cells can affect outcomes of therapy. The early stage of receptor mediated endocytosis involves the formation of transient structures known as clathrin coated pits (CCPs). This process depends on the detailed energetics of protein binding and associated membrane transformations. The CCPs either mature into clathrin coated vesicles (CCVs) or regress and vanish from the cell surface. During CCP formation, clathrin and several other proteins assemble to form a coat on the cytoplasmic side of the outer cell membrane. We previously developed a simple physical model for CCP dynamics and have carried out Monte Carlo simulations to investigate the time development of CCP size. By fitting the results of the simulations to experimental data, we have been able to estimate values of the kinetic parameters related to the formation of clathrin-associated protein complexes that comprise the coat. Recently, we have extended that model to investigate the role that CME plays in the uptake of viruses and nanoparticles (NPs). Understanding how nano-sized particles interact with the clathrin coat is important when designing NPs for biomedical purposes, as well as for developing stategies to inhibit cellular entry of viruses. Heretofore, theoretical models on this subject did not take clathrin coat assembly into explicit consideration. Thus we have developed a framework to study the endocytosis of single NPs, which focuses on protein coat assembly, and have derived a simple analytical formula for the mean internalization time of NPs, defined as the average time between the binding of a NP to the plasma membrane and its entry into the cell. We have studied the dependence of this quantity on coat parameters as well as NP size. Experiments indicate, for example, that there is a maximum size beyond which uptake via clathrin-mediated endocytosis does not occur. Moreover, there seems to be an optimal size at which cellular uptake is highest. Various published results indicate that these sizes seem to be independent of the type of cells, nanoparticles, and ligands. We have been able to show that such observations are consequences of the energetics and kinetics of protein coat formation during CCP production. As indicated above, we also have investigated putative temperature-dependent lipid phase transitions occurring in higher eukaryotes. It is well established that microorganisms adjust the lipid composition of their membranes in response to changes in the temperature at which they are grown. Moreover, investigations carried out over many years have demonstrated that whole lipid extracts from various higher organisms, as well as microorganisms, exhibit singular properties at their growth temperatures. We have investigated previously-published data concerning the temperature dependence of the electrophysiological responses of cells obtained from representative animals (e.g., frog, squid; rat), searching for unusual features occurring at the gestation/growth temperature, Tg, of these animals. Special emphasis has been given to the giant axons of the temperate squids Loligo forbesi and Loligo pealei, where the temperature dependencies of the resting potentials and action potentials exhibit behaviors that strongly suggest the onset of a membrane state change at Tg, mirroring, in the case of squids, anomalies seen in the physical properties of films formed of whole lipid extracts obtained from those organisms. Based on approximations to the classic Hodgkin-Huxley equations, analysis of axonal responses indicates that observed changes in these electrophysiological characteristics most likely reflect reversible molecular couplings between voltage-switchable ion channels and surrounding lipids in the plasma membrane, which can affect the probability of channel opening. The change in electrophysiological properties with increasing temperature for these animals yields activation energies close to values noted for other putative lipid-bilayer-linked kinetic processes which we have examined, as well as being seen in the diffusion of exogenous probes in lipid extracts (e.g., A.J. Jin, M. Edidin, R. Nossal, and N.L. Gershfeld, Biochemistry 38:13275-8, 1999). These, and other observations, substantiate the view that to first order the lipid bilayer acts as a universal solvent for the embedded, integral proteins found in the plasma membrane.